Circumference Calculator
Enter whichever value you have — radius, diameter, circumference or area — and the other three are worked out instantly, along with the surface area and volume of the sphere with the same radius.
π is used at full floating-point precision (3.141592653589793) and rounded only for display; C = πd also works directly when you know the diameter.
Formula and calculation
Worked example
A circle with a radius of 5 m has a diameter of 10 m, a circumference of 31.4159 m and an area of 78.5398 m². A sphere built on the same 5 m radius would enclose a volume of 523.5988 m³.
π is simply C ÷ d, measured on any circle
Wrap a string around any circular object, straighten it, and divide its length by the distance across the middle — every time you get the same number, 3.14159…, whether the object is a coin or a roundabout. That definition is why circumference and diameter are locked together by nothing more than a single constant, and why the circumference formula takes the two inputs it does. Archimedes trapped the constant between 3 10/71 and 3 1/7 by drawing polygons inside and outside a circle; Lambert proved in 1761 that it can never be written as a fraction of two whole numbers, so 3.14 and 22/7 are useful nicknames rather than the real thing. This calculator keeps 3.141592653589793 in the arithmetic and rounds only the answer.
Which of the four values do you actually have?
In practice the value you hold decides the sum you do. A tape measure wound around a pipe or a tree trunk gives you the circumference, and r = C ÷ 2π turns it into a radius — forestry and pipework still record sizes as girth for exactly that reason. A caliper or a ruler laid across a jar gives you the diameter, and multiplying by π is the whole calculation. A flooring or paint estimate starts from an area, and r = √(A ÷ π) is the step that turns it back into a length. Enter whichever you have; the other three come out of the same π, so they stay consistent with each other no matter which tab you use.
What the results mean
- Circumference
- The distance all the way around the circle, C = 2πr, in metres. This is the circle's perimeter, and it is what a tape wrapped around the edge would read.
- Area of the circle
- The surface enclosed by the circle, A = πr², in square metres. It is the same area you would get from the radius or the diameter directly.
- Radius
- Half the diameter — the distance from the centre to the edge. When you start from the circumference it is r = C ÷ 2π, and when you start from the area it is r = √(A ÷ π).
- Diameter
- The widest distance across the circle, straight through the centre: twice the radius, or the circumference divided by π.
- Sphere surface area
- The surface area of a sphere with the same radius, 4πr² — exactly four times the area of the circle, like the four hemispheres of a peeled orange.
- Sphere volume
- The volume of a sphere with the same radius, (4 ÷ 3)πr³, in cubic metres.
- Calculation
- The formulas with your numbers substituted in, so you can see how the radius was found and how the circumference and area followed from it.
Frequently asked questions
How do I find the circumference from the diameter?
Multiply the diameter by π: C = πd. A circle with a diameter of 12 m has a circumference of 37.69911184307752 m — about 37.7 m. You never need the radius for this one, which is why a diameter measurement and a calculator is the shortest route around.
How do I find the radius from the circumference?
Divide the circumference by 2π, which is about 6.2832. A circumference of 10 m gives a radius of 1.5915494 m — a little over half a metre. This is the calculation to use when a tape measure around a cylinder is easier than reaching the centre.
Is the circumference the same as the perimeter?
Yes. Perimeter is the general word for the distance around any shape, and circumference is the name for the same distance on a circle. So a circle with a circumference of 31.42 m has a perimeter of 31.42 m — the two never differ, only the vocabulary does.
How do I work out the area from the circumference alone?
Square the circumference and divide by 4π: A = C² ÷ 4π. A circumference of 10 m gives 100 ÷ 12.5663706 = 7.9577472 m². It is the same answer as finding the radius first (1.5915494 m) and then squaring it and multiplying by π.
Why does the calculator also show a sphere?
Because the same radius describes a ball, and the surface area and volume of that ball are natural follow-ups: surface = 4πr² and volume = (4 ÷ 3)πr³. For r = 5 m that is 314.1592654 m² of surface and 523.5987756 m³ of volume — the surface area is exactly four times the area of the circle.